A blogger for Motley Fool is predicting a blowout quarter for Apple. He writes,

Apple is asking shoppers to pay a 65% premium — which they are, gladly.

You can put me in that group.

Millions of consumers agree. By my math, the Mini probably brought in $2.2 billion in operating profit in fiscal Q1,

These are big claims. Note that he is predicting $2.2 billion profit from just one product line and that too operating profit not gross margin. Just as a refresher, gross margin is revenue less Cost of Goods Sold (COGS) for that product line. Operating profit is after R&D, sales & marketing and other operational expenses.

In the last quarter Apple made $11B in operating profit, so Motley Fool is predicting 20% increase over last quarter just due to iPad mini.

What is the basis for this? Well we know this blogger bought one and hence he believes millions did so as well. But after that we do not know how he did his math to show $2.2B as operating profit.

Well I did some math as well, about three months ago, and published my math, model and assumptions. In my last article in GigaOm I wrote (these are numbers for full year, not just Q1),

At the low end they could possibly lose $1.7 billion and at the high end they could make $2.5 billion in profit. But the chances of both these scenarios are just 1 percent. And so realistically, considering all possible scenarios, the expected value of profit is half a billion dollars—and that is gross profit, not including marketing and other costs associated with iPad mini.

From my more rigorous statistical modeling I predicted the best case scenario is $2.5 billion **gross margin for the entire year** and the chances of that happening are just 1%. So for Q1 numbers let us assume even distribution and divide my numbers by 4. That gives $125 million as expected profit and $625 million as 1% possibility.

How can Motley Fool predict such large numbers?

The first difference is I did statistical modeling that considered all possible scenarios and not just the best case scenario. If Motley Fool assumed,

“I bought it, so millions would buy”

Of course it would yield $2.2B but that fails to say how likely is such a scenario. Only in statistical modeling we can not only state an outcome but also state how likely is that scenario. (You heard of Nate Silver?)

Second difference is I took into account the negative effect of iPad mini on other product lines. That is iPad mini is not all additive, there is cannibalization. Using customer research data I included that effect (accounting for the uncertainty in the cannibalization rate) in computing net profit from iPad mini.

Finally I am not sure if Motley Food did any math at all. They say Apple would sell 20 million total iPad units (mini and maxi?). Since last quarter Apple sold 15.4 million iPads last quarter that would mean 4.6 million iPad mini (and by their assumption there was no cannibalization). So $2.2B in operating profit from mere 4.6 million units.

That is each unit contributed $478 in operating profit. Really? Far more than the likely ASP of iPad mini and more than gross profit from iPad line. What kind of investment analysis or math is that? I hear this site gives investment advice, I wonder.

Lastly, I do stand by my model. Just wait a week more and plug in the numbers from Apple’s earnings report into this model and find out.

**Note**: Some have pointed out in GigaOm comments section that I used too conservative a number for iPad per unit profit and that iSuppli had a different (higher) margin prediction. My mean was 32% with sigma of 4.6% while iSuppli says the numbers are 42%. Even if I adjusted my mean to use iSuppli numbers, my predicted BEST CASE (2% chance) gross profit will utmost go to $0.8B per quarter and not $2.2B Motley Fool predicts.

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